- #1

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Write and equation to model this.

so 25% is left in his body that means that 75% was used up.

so 25%, 125%, !50%

...thats wrong right?

I dont know what to do...

- Thread starter Aya
- Start date

- #1

- 46

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Write and equation to model this.

so 25% is left in his body that means that 75% was used up.

so 25%, 125%, !50%

...thats wrong right?

I dont know what to do...

- #2

- 172

- 2

Six hours later, he has (0.25 x 500)mg of medicine from the previous round remaining in his body, as well as another dosage of 500mg.

Another six hours later, he has (0.25)(0.25 x 500 +500)mg of medicine from the previous rounds remaining in his body, as well as another dosage of 500mg.

Try to observe a pattern here and see if you can fit a certain distribution into part of your final equation!

- #3

HallsofIvy

Science Advisor

Homework Helper

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To "relive" the pain?? What an evil doctor!Aya said:

Write and equation to model this.

so 25% is left in his body that means that 75% was used up.

so 25%, 125%, !50%

...thats wrong right?

I dont know what to do...

What's right with it? What do 25%, 125%, 150% mean? You were asked to write an equation and that is not an equation! Let f(t) be the amount of medication in his body, in mg, after t hours. You knowso 25%, 125%, !50%

...thats wrong right?

f(0)= 500 and f(6)= (0.25)(500)= 125. That's not enough to information without at least knowing the "type" of function. The simplest assumption is that f(t) is

Then f(0)= m(0)+ b= b= 500 and f(6)= m(6)+ b= 125. Find m and b.

A more realistic assumption would be an "exponential function": f(t)= Ca

Now,

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- #4

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so what I was doing was finding the % of medicnin that was in his body, but I guess this approach was wrong

So I have to find the amount of medicin that is in his body

So...

t0=5oomg

t1=625mg

t2=656.25

Then

tn-1 x 0.25+500

would be the recursave fomula

- #5

- 172

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You are right in saying that the recursive formula is [tex]T_{n}=0.25T_{n-1}+500[/tex]. However, this formula needs you to know what [tex]T_{n-1}[/tex] is before you can find out the value of [tex]T_{n}[/tex]. Is it possible for you to find a formula which expresses [tex]T_{n}[/tex] in terms of n?

Here are some steps to guide you:

Let [tex]T_{n}[/tex] be the amount of medicine in Tod's body 6n hours after the first dosage.

So, [tex]T_{0}=500[/tex]

[tex]T_{1}=500(0.25)+500[/tex]

[tex]T_{2}=0.25(500(0.25)+500)+500[/tex]

...

Work out an expression for [tex]T_{3}[/tex] but do not simplify it. Some re-arrangement of terms in the expressions obtained should be helpful. Then try to obtain a general equation of [tex]T_{n}[/tex] in terms of n and see if you can fit a certain series into PART of the equation. (On first glance, which series do you think is involved? If this series is involved, what should the terms in the series look like?)

Here are some steps to guide you:

Let [tex]T_{n}[/tex] be the amount of medicine in Tod's body 6n hours after the first dosage.

So, [tex]T_{0}=500[/tex]

[tex]T_{1}=500(0.25)+500[/tex]

[tex]T_{2}=0.25(500(0.25)+500)+500[/tex]

...

Work out an expression for [tex]T_{3}[/tex] but do not simplify it. Some re-arrangement of terms in the expressions obtained should be helpful. Then try to obtain a general equation of [tex]T_{n}[/tex] in terms of n and see if you can fit a certain series into PART of the equation. (On first glance, which series do you think is involved? If this series is involved, what should the terms in the series look like?)

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